Not the religious kinds, either Conversions Not the religious kinds, either

Why Why Why? Why do we do conversions? How do we do conversions? teachers are mean not entirely really for real world value cooking how many cups in a quart trip to Paris miles per hour to kilometers per hour How do we do conversions? number line dimensional analysis

The Conga Number Line M - - k - - base - c m - -  - - n If we use the number line, it goes something like this: count the number of spaces from one unit to the other move your decimal the same number of places, in the same direction The number line looks like this: M - - k - - base - c m - -  - - n

The players M - - k - - base - c m - -  - - n M = Mega k = kilo base = base units c = centi m = milli  = micro n = nano NOTE: c m (below) is not centimeters! M - - k - - base - c m - -  - - n

Da da da da da, dun M - - k - - base - c m - -  - - n Let’s convert 4000 km to m That’s kilometers to meter Base unit is . . . the meter 1st, we find the unit we coming from k Next, we find where we’re going base Count the spaces between, noting the direction 1 2 3 Start M - - k - - base - c m - -  - - n

Conga! 4000. km = 4000000 m So we went 3 spaces, to the right Move your decimal three places to the right You will find: 4000. km = 4000000 m But what do we do? fill in the blanks with zeros!

But the fat lady isn’t singing What if we want to convert km to miles? or days to hours or to minutes Number line is a sophomoric method, we use dimensional analysis I would bet you already do this, but don’t realize it! If you can tell me how many hours are in three days, you can!

That’s a fancy word Mr. Bitzer Relax, it’ll be okay. We’ll start with an easy one How many hours are in 3 days? First, we need to know how days and hours are related Hopefully, we know that there are 24 hours in a day If we write this using math, 24 hours = 1 day this is called a unity conversion, because something = 1

Wait a minute! So we know that 1 day = 24 hours; we want to know how many hours are in 3 days but we just multiply 3*24 = 72; that’s easy! How’d you know to do that? Let’s set it up: Our unity conversion goes here 3 days ? hrs What we’re trying to convert What we’re converting to

But what goes where? 3 days ? hrs 1 day 24 hr 24 hr 1 day We know we use 1 day = 24 hour, but how? We want days to cancel, and be left with hours Let’s try it So the days cancel, and we’re left with hours Now we simply do what the fraction tells us If we had a number on the bottom, we would simply divide Does anything cancel? NO! Uh oh :-( Try it the other way now!

The answer: 3 days 24 hr 1 day 3*24 / 1 = 72 hrs I know it seems like this is a hard way now, but it’s much easier once you get the hang of it When using the metric system, you should know the exponents from the beginning of the year (pg 17 in your book)

Powers that be nano = 10-9 micro = 10-6 milli = 10-3 centi = 10-2 kilo = 103 Mega = 106 We should know these, but if not, know is a good time to learn. We use these by saying 1 cm = 10-2 m Or we say 1 kg = 103 g Replace the prefix with the appropriate power 1 Mm =1 mega meter = 106 m

Back to our original example Our conversion goes here 4000 km = ? m 4000 km 1 km ? m What we’re trying to convert 103 m What we’re converting to We’re converting 4000 km to meters We know 1 km = 103 m Again, set it up so the units cancel This isn’t right!

Try number two: This is right! The km cancel Our conversion goes here 4000 km = ? m 4000 km 1 km 103 m 4000 x 103 m What we’re trying to convert What we’re converting to This is right! The km cancel We’re left with m this is what we want See this is the same thing as before!

Conversions This is the way that we will do conversions There is no way to forget the number line The only thing to remember are those 7 prefixes from the previous slide

One last example . . . Let’s convert 4000 g to kg Set it up yourself: We’re starting from grams (the base) We’re going to kilo Set it up yourself:

You should have: You would divide 4000 by 103 and you will get . . . 1 kg 103 g 4 m You would divide 4000 by 103 and you will get . . .

Not just for simple conversions We can also convert 100 km/hr to m/sec first convert km to m, then hr to sec 1 km 103 m 100 km hr 1 hr 60 min 1 min 60 sec 100* 103 m 60*60 sec 100000 m 3600 sec 27.78 m/sec

Works for any conversion Now we can handle conversion such as kilometers to miles, if we know the unity conversion 1 mi = 1.61 km Or pounds to Newtons 1 lb = 4.45 N remember, pound is not a measurement of mass! Or inches to cm 1 in = 2.54 cm

Convert everything you can Go forth and multiply or divide Go door to door, trying to convert people or things If there are questions, tutoring is available thru MAO, NHS, or Mr. Bitzer MAO = Wednesdays second half NHS = Tuesdays second half Mr. Bitzer = Monday, Wednesday mornings